This paper describes a new method of lossy still-image compression, called adaptively scanned wavelet difference reduction (ASWDR). The method produces an embedded bit stream with region- of-interest capability. It is a simple generalization of the compression method developed by Tian and Wells, which they have dubbed wavelet difference reduction (WDR). While the WDR method employs a fixed ordering of the positions of wavelet coefficients, the ASWDR method employs a varying order that aims to adapt itself to specific image features. This approach enables ASWDR to outperform WDR in a rate- distortion sense, and to essentially match the rate-distortion performance of the widely used codec SPIHT of Said and Pearlman. ASWDR compressed images exhibit better perceptual qualities, especially at low bit rates, than WDR and SPIHT compressed images. ASWDR retains all of the important features of WDR: low complexity, region-of-interest capability, embeddedness, and progressive SNR.